Formula from Chapter 4: finding the limiting reactant
\(n_{\mathrm{\ce{->}}} = \mathrm{min}(\dfrac{n_{\mathrm{reactant}}}{ν_{\mathrm{reactant}}}, ...)\)
You can use this if: you know the amount of all the reactants and you have a balanced chemical equation
\(\ce{2 H2}\)\(\ce{ + }\)\(\ce{O2}\)\(\ce{->}\)\(\ce{2H2O}\)\(\ce{ }\)
\(ν_{\mathrm{\ce{H2}}}\) \(= 2\) stoichiometric coefficent of hydrogen molecules
\(n_{\mathrm{\ce{O2}}}\) \(= 0.53\ \mathrm{mol}\) chemical amount of oxygen molecules (dioxygen)
\(ν_{\mathrm{\ce{O2}}}\) \(= 1\) stoichiometric coefficent of oxygen molecules
\(n_{\mathrm{\ce{->}}}\) \(= \mathrm{min}(\dfrac{n_{\mathrm{\ce{H2}}}}{ν_{\mathrm{\ce{H2}}}}, \dfrac{n_{\mathrm{\ce{O2}}}}{ν_{\mathrm{\ce{O2}}}})\) chemical amount of reaction
\(\ \ \ =\mathrm{min}(\dfrac{3.18\ \mathrm{mol}}{2}, \dfrac{0.53\ \mathrm{mol}}{1})\)
\(\ \ \ =\mathrm{min}(1.5900\ \mathrm{mol}, 0.530\ \mathrm{mol})\)
\(\ \ \ =0.53\ \mathrm{mol}\)